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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Error estimates for spatially discrete approximations of semilinear parabolic equations with initial data of low regularity


Authors: M. Crouzeix, V. Thomée and L. B. Wahlbin
Journal: Math. Comp. 53 (1989), 25-41
MSC: Primary 65N10
MathSciNet review: 970700
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Abstract: Semidiscrete finite element methods for a semilinear parabolic equation in $ {R^d}$, $ d \leq 3$, were considered by Johnson, Larsson, Thomée, and Wahlbin. With h the discretization parameter, it was proved that, for compatible and bounded initial data in $ {H^\alpha }$, the convergence rate is essentially $ O({h^{2 + \alpha }})$ for t positive, and for $ \alpha = 0$ this was seen to be best possible. Here we shall show that for $ 0 \leq \alpha < 2$ the convergence rate is, in fact, essentially $ O({h^{2 + 2\alpha }})$, which is sharp.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1989-0970700-7
PII: S 0025-5718(1989)0970700-7
Article copyright: © Copyright 1989 American Mathematical Society